The invention relates to the correction of the carrier frequency at the receiving end in a packet transmission system.
The invention finds important applications, notably in the synchronization of multi-user transmission systems by way of satellite or cables with return paths, in which a plurality of terminals are capable of transmitting data packets to a head station in accordance with a frequency and time-division multiplex system.
These terminals are generally intended for consumers. It is thus important to reduce their cost price. It is therefore advantageous to use low-cost local oscillators, i.e. relatively inaccurate oscillators, for generating the carrier frequencies to be used in the transmissions from the terminals to the head station, usually referred to as ascending transmissions. Typically, the oscillators used have an accuracy which varies between 1 ppm and 10 ppm. The resultant error in the generated carrier frequency is proportional to the carrier frequency and is larger as the frequencies used are higher. For example, in the satellite transmission systems which use the frequency band Ka (20 GHz-30 GHz) for the ascending transmissions, the difference or frequency error observed for a local oscillator having an accuracy of 1 ppm may reach +30 kHz (i.e. for a symbol frequency of 100 kHz, the normalized frequency difference with respect to the symbol frequency is +30%).
The article xe2x80x9cFeedforward Frequency Estimation for PSK: a tutorial reviewxe2x80x9d by M. Morelli and U. Mengali, published in the magazine European Transactions on Telecommunications, volume 9, no. 2, March-April 1998, pages 103-106 describes a frequency estimator which is based on an algorithm named after its authors Rife and Boorstyn for estimating a frequency error between the carrier at the transmitting end and that at the receiving end. This error is within a normalized frequency range of xc2x1xc2xd with respect to the symbol frequency xcex94f/B (in which xcex94f is the frequency error and B is the symbol frequency). In the description hereinafter, the estimation of the normalized frequency distance to be determined (equal to xcex94f/B or to xcex94fxc3x97TS where TS is the duration of the symbol) will be denoted as xcex94{circumflex over (f)}.
The carrier frequency estimators may be characterized by different parameters, notably the accuracy of the estimation obtained, the size of the acquisition range of the frequency difference, denoted xc2x1xcex94fmax, the minimum level of the signal-to-noise ratio SNR of the treated signal, and the complexity of the algorithm. Some of these parameters have opposed evolutions. Particularly, the accuracy of the estimation is smaller as the acquisition range xc2x1xcex94fmax is larger, with an equal complexity. On the other hand, the estimators are all the more complex as they are capable of functioning at low signal-to-noise ratios. Rife and Boorstyn have shown that the frequency error xcex94{circumflex over (f)} (or xcex94fxc3x97TS) has a maximum probability of being situated on both sides of the maximum of the amplitude with the following discrete function, denoted Z(xcex94{circumflex over (f)}):                               Z          ⁡                      (                          Δ              ⁢                              xe2x80x83                            ⁢                              f                ^                                      )                          =                              1            L                    ⁢                                    ∑                              k                =                0                                            L                -                1                                      ⁢                          xe2x80x83                        ⁢                                          z                ⁡                                  (                  k                  )                                            xc3x97                              ⅇ                                                      -                    j                                    ⁢                                      xe2x80x83                                    ⁢                  2                  ⁢                  nk                  ⁢                                      xe2x80x83                                    ⁢                  Δ                  ⁢                                      xe2x80x83                                    ⁢                                      f                    ^                                                                                                          (        1        )            
in which L is the observation length, i.e. the number of received symbols used for computing the error estimation,
k represents the position of the symbol in the received packet,
with z(k)=r(k)/ck* if the received symbols are known, where ck* is the conjugated complex of the predetermined known symbol ck and where r(k) is the symbol received with a frequency error xcex94f with r(k)=ckxc3x97ej(2xcfx80.kxcex94fTS+xcfx860)+n(k) where xcfx860 is the initial phase shift between the local oscillator used at the receiving end and that used at the transmitting end (this phase shift may be different for each packet and may correspond to the phase shift for k=0) and where n(k) represents the noise in the channel,
and with z(k)=ejM arg|r(k)| if the symbols received are not known in advance, where M is the number of phases of the used modulation of the type PSK (Phase Shift Keying) but in this case the result obtained must be divided by M for obtaining the estimation xcex94{circumflex over (f)}.
It is particularly an object of the invention to provide a more accurate estimation of the frequency error in a packet transmission system in which the data packets can be transmitted by different transmitters and are susceptible to different frequency shifts at the receiving end. The frequency correction method according to the invention is of the semi-NDA type (Non-Data Aided) i.e. it does not use known data for realizing the frequency error estimation but, in contrast, requires only a previously effected phase error estimation. This method is thus particularly suitable for packet transmission systems without a preamble and is adapted to the signals which are modulated in accordance with a phase modulation of the PSK type as well as to signals which are modulated in accordance with a quadrature amplitude modulation of the QAM type (Quadrature Amplitude Modulation).
To this end, the invention provides a method of estimating the frequency at the receiving end for a packet transmission system, for estimating a carrier frequency error between received symbols (rk) and transmitted symbols (ck). The method comprises the computation of an error function (H(xcex94{circumflex over (f)})) for error values (xcex94{circumflex over (f)}) comprised in an acquisition interval ([xe2x88x92fmax, +fmax]). It derives therefrom an estimation (xcex94{circumflex over (f)}0) of said carrier frequency error. The error function (H(xcex94{circumflex over (f)})) is defined for minimizing a magnitude which is representative of an average distance between the received symbols which are compensated in phase (rxe2x80x2k) and estimations (ĉkej2xcfx80kxcex94{circumflex over (f)}) of the received symbols affected by a frequency error estimation. These are obtained by varying the frequency error (xcex94{circumflex over (f)}) in the acquisition interval ([xe2x88x92fmax, +fmax]) for estimations of the transmitted symbol (ĉk). These estimations of the transmitted symbol (ĉk) are obtained by means of a decision based on a threshold relating to the received symbol which is compensated in phase (rxe2x80x2k). For a modulation of the QPSK type (Quadrature PSK), the threshold decision is made on the basis of the sign of the real and imaginary parts of the received, phase-compensated symbol (rxe2x80x2k).
It is possible to obtain a good performance with the invention when the frequency error to be estimated is low, of the order of 1%. For this reason, when the real error is more important, the method according to the invention will be preferably effected after a first estimation of the frequency error computed in accordance with a conventional method of the DA type (Data Aided) using, if possible, data from the preamble of the transmitted packets or, if the packets do not have a preamble, a method of the NDA type as described in the quoted article. The residual error may then be advantageously estimated by means of the method according to the invention.
In a transmission system in which the data packets may originate from different transmitters having different frequency errors and in which each transmitter transmits at distinct instants and is susceptible of transmitting each packet with a different error, it is not possible to correct the frequency error continuously. For example, the receiver in the head of the network must perform a correction on each received packet. However, there is a probability that the frequency errors for a given transmitter vary more or less in accordance with a function which is more or less known or can be fairly easily approximated. For this reason it is interesting to use the estimation computed for the last packet or packets transmitted by a given transmitter for fixing the acquisition range of the error to be corrected in the next packet.
In accordance with a characteristic feature of the invention the acquisition range ([xe2x88x92fmax, +fmax]) may be fixed for a given transmitter as a function of the estimation which has been previously computed for the packets received from this transmitter.